We study the normal form of multipartite density matrices. It is shown that the correlation matrix (CM) separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the entanglement wi
tness is further constructed in terms of local orthogonal observables for both bipartite and multipartite systems.
We classify biqutrit and triqutrit pure states under stochastic local operations and classical communication. By investigating the right singular vector spaces of the coefficient matrices of the states, we obtain explicitly two equivalent classes of
biqutrit states and twelve equivalent classes of triqutrit states respectively.
We investigate the separability of arbitrary dimensional tripartite sys- tems. By introducing a new operator related to transformations on the subsystems a necessary condition for the separability of tripartite systems is presented.
We investigate the separability of quantum states based on covariance matrices. Separability criteria are presented for multipartite states. The lower bound of concurrence proposed in Phys. Rev. A. 75, 052320 (2007) is improved by optimizing the local orthonormal observables.
We generalize the Schmidt-correlated states to multipartite systems. The related equivalence under SLOCC, the separability, entanglement witness, entanglement measures of negativity, concurrence and relative entropy are investigated in detail for the generalized Schmidt-correlated states.
